Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C34 · Schur multiplier (H2) = C23×C35 |
| direct product | C23×H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C34 |
| commutator, Frattini, cosocle | C3 | C23×C34 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
4688 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(7,8,11)(9,15,26)(10,14,21)(12,22,17)(13,25,19)(16,28,32)(18,24,20)(23,33,29)(27,31,30);(3,4)(7,9,16)(8,12,23)(10,18,29)(11,20,31)(13,24,28)(14,15,27)(17,30,19)(21,22,32)(25,26,33);(5,6)(9,17,18)(12,24,15)(16,29,30)(20,26,22)(23,27,28)(31,32,33);(8,13,14)(11,21,25)(12,24,15)(20,22,26)(23,28,27)(31,32,33)664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3780);